For instance, Seto et al. [1]} proposed that using the DECihertz Interferometer Gravitational wave Observatory (DECIGO) to observe BNS merger during about a 10-year observation could measure the phase and frequency evolutions of GW signal which are proportional to \(H(z)\) . However, this approach strongly depends on the knowledge of waveform and is limited by the estimation error on the individual source mass. Another approach of directly measuring \(H(z)\)  through GW observation is to use dipole components of luminosity distance arising from the matter inhomogeneities of large-scale structure and the local motion of observer [2]}. This idea was proposed by Bonvin et al. [3]}, [4]} for the SN Ia observation, and further developed by Nishizawa et al. [5]} for the GW observation.
